Hi Clyde95 and welcome to the forum,
I've added a new entry for the Cayley cubic surface (thanks for pointing me to this interesting surface). I used two implicit representations of the Cayley Cubic surfaces to obtain the attached images. You have to save the attached script as, for example, cayley.k3ds and import it into K3DSurf by using the "Load" button. You will then have two new implicit entry in the "Examples" list.

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Can the upper equation be converted to a parametric equations?

I don't think there is a parametric representation of the Cayley Cubic.

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I am not even sure I found the right isosurface equation

Cayley Cubic, Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface are all part of the Cubic surfaces family but the subject if far more complex than it first looks...for me too _________________Cheers,
Abderrahman

Hi,
The Parametrization of an implicit equation is not always possible but , in some cases, this process can be carried out as an exact match (or as an approximation) to the parametric equation.
So, first of all, you should find out if your implicit form can be converted to a parametric form and after that, try to make the conversion itself.
There are some implicit forms that can be "easily" converted and to find out which one, you can do some google search with , for example, "how to convert implicit surfaces to parametric form?".
There are plenty of PDF manuals available for free but I'm afraid most of theme requires some good knowledge of the subject...
So, as you see, here too, the subject is more complex than it first look!_________________Cheers,
Abderrahman

Ah, yes this looks like something too complicated for my knowledge of mathematics.
Do you think Cayley Cubic surface's implicit equation could somehow be converted an parametric one? How would it look like?
Thank you.